Generalized augmented Lagrangian methods for equality constrained optimization problems

In this paper we consider generalized augmented Lagrangian methods including a classical augmented Lagrangian method and some " lower order" augmented Lagrangian methods as special cases for a mathematical program with only equality constraints. Since generalized augmented Lagrangians are in general not differentiable or even not locally Lipschitz, we carry out convergence analysis of first-order and second-order stationary points of generalized augmented Lagrangian methods by applying the Borwein-Preiss approximate smooth variational principle.